Wave Phase

Alright. Let's talk about wave phase. Wave phase is kind of a strange idea but it turns out to be very very very useful and not really that difficult once we understand what it means.

The word phase is used to describe a specific location within a given cycle of a periodic wave. So when I look at a periodic wave, here I've got two cycles. Now point a, point b, point c, point d, point e and so on don't represent the same place within the cycle that goes from a to g, they just don't. So we want to be able to talk about the relationship between a and other parts of another wave of that later cycle that are kind of the same thing as a. So if it's the same thing, we say that they're in phase. So let's look at this.

Alright. So we got point a. What other points are in phase with point a? Well, point d is at the same place but the wave's not doing the same thing. Here the wave's going up, here the wave's going down. So a and d are not in phase. They're at different phase, alright? What about, well, it's obvious that b, c, e and what about g?

Well, at g we've got same place doing same thing. So a and g will be in phase, alright? Let's look at point b. Point b is a easy one because it's a peak. Any time you're at a peak, there's only one place on the wave where you can get to that peak. So any place you're at the peak, you're in phase. Good enough. Obviously f is not and it's kind of the opposite. Alright? and we'll talk about that in a minute.

What about point c? Well, for point c, we've got two possibilities, h and j. Now with h, it's at the same location but again it's not doing the same thing. So c and h are not in phase but c and j are. Alright. Fairly simple but trust you understand it. Just look. Same place, doing same thing, in phase. Alright.

So why do we care about this? Well, a wavelength can be defined as the distance between any two consecutive locations that are in phase with each other. So that's kind of nice. It means I don't need a crest and a crest or a trough and a trough, I just need phase, same phase, done. Wavelength. What if they're out of phase? They're out of phase, we'll use some trig to describe how far they are out of phase. So just like our standard sine and cosine graphs, we're going to take the whole wave as being 360 degrees or if we're using radiants we use 2 pi. But let's just go ahead and work in degrees for now.

So what about a and b? They're clearly not in phase, so how far out of phase are they? So the question, let me rephrase it is, how far do I need to go inside the wave to go from a to b? Alright. Well, the easiest way to look at this, is as a fraction of the wave length which is really what phase is doing. So the wavelength is all the way from here to here. Now, half the wavelength is that, so this would be a quarter of the wavelength. A quarter of 360 degrees is 90 degrees. So we would say that a and b are 90 degrees out of phase, alright? What about a and c? Well a and c are crest and trough. Now in this case, it's a whole half wavelength out of phase. so we would say 180 degrees out of phase.

Now a and c are actually opposites in some sets. So, instead of saying 180 degrees out of phase, sometimes people say they are completely out of phase. Alright? a and d, well, here we got to go all the way here then this whole thing so we could say 270 degrees out of phase. But we could also say a and e are in phase and d is just 90 degrees backwards. So we could either say 270 degrees out of phase or we could say 90 degrees out of phase in the other direction. Or -90 degrees out of phase. Alright? That's phase.